IB Maths AI SL AI 4.4 Hypothesis testing and confidence intervals questions

An environmental field team compared aquatic indicator-plant abundance in one restored wetland and one unrestored wetland. At each wetland, 60 quadrats were selected at random. The number of indicator-plant species in each quadrat was classified as low, medium or high.

(a) Calculate the expected frequencies for all six cells if wetland type and abundance class are independent. State whether the expected-frequency condition for a chi-squared test is satisfied. [2]

(b) For a chi-squared test of independence at the 5% significance level, state H₀ and H₁, give the degrees of freedom, and use your GDC to find the chi-squared statistic and p-value. [5]

Dissolved oxygen was measured in a randomly selected subset of 24 quadrats at each wetland. The summary statistics were:

Before collecting the data, the team predicted that the mean dissolved oxygen concentration would be higher at the restored wetland. Assume that the two samples are unpaired, the underlying populations are normal, and their unknown variances are equal.

(c) For the comparison of mean dissolved oxygen concentrations,

(i) write down H₀ and H₁ for the team’s prediction. [2]

(ii) Use a pooled two-sample t-test on your GDC to find the one-tailed p-value for this prediction and the two-tailed p-value. [2]

(d) At the 5% significance level, assess an officer’s claim that the fieldwork proves restoration caused an improvement in wetland quality. Use the results and the fieldwork design in your answer. [3]

A field ecologist investigates whether bee visits differ between a mown and an unmown meadow. There is one meadow of each type. For the first investigation, 30 distinct bee visits were randomly selected from each meadow and classified by duration.

For a separate investigation, a random sample of 12 distinct bee visits was taken from each meadow. The sample means and sample standard deviations of visit duration were as follows.

Assume the two populations of visit durations are normally distributed, have equal variances, and were sampled independently. Use a 5% significance level for each test.